AnswersPrecalculusPractice TestQuestion 1
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Question 1 • Precalculus

What is the exact value of sine of open paren 105 degrees close paren ?

Answer
A
negative the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2
B
the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2
C
the fraction with numerator square root of 2 plus square root of 3 end root and denominator 2
D
negative the fraction with numerator square root of 2 minus square root of 3 end root and denominator 2

Explanation

Use the angle-sum identity: sin(105°) = sin(60° + 45°) = sin 60° cos 45° + cos 60° sin 45°. Substituting the exact values gives (√3/2)(√2/2) + (1/2)(√2/2) = (√6 + √2)/4, which is also √(2 + √3)/2. This matches choice A.

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